Question
The graph shows the distance a ghost crab can run over time.

Let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation (y=kx) for this relationship?
A
d=35td=\frac{3}{5}td=53t
B
d=53td=\frac{5}{3}td=35t
C
t=53dt=\frac{5}{3}dt=35d
D
t=25dt=\frac{2}{5}dt=52d

Let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation (y=kx) for this relationship?
A
d=35td=\frac{3}{5}td=53t
B
d=53td=\frac{5}{3}td=35t
C
t=53dt=\frac{5}{3}dt=35d
D
t=25dt=\frac{2}{5}dt=52d
Answers
GPT-4o mini
A direct variation equation has the form \( d = kt \), where \( k \) is the constant of proportionality.
To find which answer corresponds to this form, we need to look for an equation where distance \( d \) is expressed in terms of time \( t \) with a constant \( k \).
Among the options provided:
- **Option A:** \( d = 35t \) (This is in the correct form.)
- **Option B:** \( d = \frac{5}{3}t \) (This is also in the correct form.)
- **Option C:** \( t = \frac{5}{3}d \) (This is not in the correct form; it's inverted.)
- **Option D:** \( t = \frac{2}{5}d \) (This is also not in the correct form; it's inverted.)
Therefore, both Option A and Option B are valid direct variation equations. Without additional context about the graph, either could be correct based on the value of the constant \( k \).
If you need only one answer, and assuming we stick to the context typically surrounding ghost crabs, **Option A \( d = 35t \)** seems like a reasonable representation for their running distance since both options A and B could be valid depending on the constants given. Please ensure the correct choice based on the information provided within the graph itself.
To find which answer corresponds to this form, we need to look for an equation where distance \( d \) is expressed in terms of time \( t \) with a constant \( k \).
Among the options provided:
- **Option A:** \( d = 35t \) (This is in the correct form.)
- **Option B:** \( d = \frac{5}{3}t \) (This is also in the correct form.)
- **Option C:** \( t = \frac{5}{3}d \) (This is not in the correct form; it's inverted.)
- **Option D:** \( t = \frac{2}{5}d \) (This is also not in the correct form; it's inverted.)
Therefore, both Option A and Option B are valid direct variation equations. Without additional context about the graph, either could be correct based on the value of the constant \( k \).
If you need only one answer, and assuming we stick to the context typically surrounding ghost crabs, **Option A \( d = 35t \)** seems like a reasonable representation for their running distance since both options A and B could be valid depending on the constants given. Please ensure the correct choice based on the information provided within the graph itself.